# CHANGING THE BASE OF A LOGARITHM - Problem 1

Let a, b, and x be positive real numbers such that neither a nor b equals 1 (remember x must be greater than 0). Then can be converted to the base b by the formula

.

Problem 1: Find .

Answer: -11.191753

Solution 1: Convert to base 10 logarithms.

Check: Let's check your answer. If , then the answer is correct.

is not exact but close enough for our check. Remember why it is not exact in the check. the -11.18900388 was rounded; therefore, the answer won't be exact.

Solution 2: Convert to base e logarithms.

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Author: Nancy Marcus

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